The new Windows default requires administrative access to install software downloaded from the print server when using the Windows Point and Print feature, you know this software as the print driver.
Microsoft does permit a new registry setting to allow a standard user to install the software.
A GPO which has worked for years will no longer work based on the new default in Windows.
If you would like to allow standard users the ability to download and install the software from the print server please review the Microsoft article to accomplish this. https://support.microsoft.com/en-gb/topic/kb5005652-manage-new-point-and-print-default-driver-installation-behavior-cve-2021-34481-873642bf-2634-49c5-a23b-6d8e9a302872
Please read the article. The registry setting is a DWord RestrictDriverInstallationToAdministrators in HKEY_LOCAL_MACHINE\Software\Policies\Microsoft\Windows NT\Printers\PointAndPrint
When the key does not exist or the value for a manually added key is 1, this prevents the software installation by a standard user.
If you have preinstalled the driver on the client and ALL the files exactly match the file set which is installed on the server, then the driver will be copied from the server and the spooler will compare the files and should throw away the software downloaded from the server.
There is a log file to determine why this may fail. C:\Windows\INF\setupapi.dev.log.
Look for !!! in the log and this should identify which file(s) is causing the mismatch.
Adding a printer is per user. A connection to a shared printer added for user1 will NEVER be seen by user2. User2 will need to add the connection in their security context.